1. Field of the Disclosure
The present disclosure relates generally to determining geological properties of subsurface formations using Nuclear Magnetic Resonance (“NMR”) methods for logging boreholes, particularly for reducing a data set using a data adaptive down-sampling scheme.
2. Description of the Related Art
A variety of techniques are currently utilized in determining the presence and estimation of quantities of hydrocarbons (oil and gas) in earth formations. These methods are designed to determine formation parameters, including among other things, the resistivity, porosity and permeability of the rock formation surrounding the borehole drilled for recovering the hydrocarbons. Typically, the tools designed to provide the desired information are used to log the borehole. Much of the logging is done after the well bores have been drilled. More recently, boreholes have been logged while drilling, which is referred to as measurement-while-drilling (MWD) or logging-while-drilling (LWD).
One commonly used technique involves utilizing Nuclear Magnetic Resonance (NMR) logging tools and methods for determining, among other things, porosity, hydrocarbon saturation and permeability of the rock formations. The NMR logging tools are utilized to excite the nuclei of the fluids in the geological formations surrounding the borehole so that certain parameters such as nuclear spin density, longitudinal relaxation time (generally referred to in the art as T1) and transverse relaxation time (generally referred to as T2) of the geological formations can be measured. From such measurements, porosity, permeability and hydrocarbon saturation are determined, which provides valuable information about the make-up of the geological formations and the amount of extractable hydrocarbons.
The NMR tools generate a static magnetic field in a region of interest surrounding the borehole. NMR is based on the fact that the nuclei of many elements have angular momentum (spin) and a magnetic moment. The nuclei have a characteristic Larmor resonant frequency related to the magnitude of the magnetic field in their locality. Over time the nuclear spins align themselves along an externally applied static magnetic field creating a macroscopic magnetization, in short: magnetization. This equilibrium situation can be disturbed by a pulse of an oscillating magnetic field, which tips the spins with resonant frequency within the bandwidth of the oscillating magnetic field away from the static field direction. The angle θ through which the spins exactly on resonance are tipped is given by the equation:θ=γB1tp/2  (1)where γ is the gyromagnetic ratio, B1 is the magnetic flux density amplitude of the sinusoidally oscillating field and tp is the duration of the RF pulse.
After tipping, the magnetization precesses around the static field at a particular frequency known as the Larmor frequency ω0 given byω0=γB0  (2)where B0 is the static magnetic flux density. For hydrogen nuclei γ/2π=4258 Hz/Gauss, so that a static field of 235 Gauss would produce a precession frequency of 1 MHz. At the same time, the magnetization returns to the equilibrium direction (i.e., aligned with the static field) according to a characteristic recovery time known as the “spin-lattice relaxation time” or T1. T1 is controlled by the molecular environment and is typically one millisecond to several seconds in rocks.
At the end of a θ=90° tipping pulse, spins on resonance are pointed in a common direction perpendicular to the static field, and they precess at the Larmor frequency. However, because of inhomogeneity in the static field due to the constraints on tool shape, imperfect instrumentation, or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. Hence, after a time long compared to the precession period, but shorter than T1, the spins will no longer be precessing in phase. This de-phasing occurs with a time constant that is commonly referred to as T2*. Dephasing due to static field inhomogeneity can be recovered by generating spin echoes (see below). The remaining dephasing is characterized by the time constant T2 and is due to properties of the material.
A receiving coil is designed so that a voltage is induced by the precessing spins. Only that component of the nuclear magnetization precesses that is orthogonal to the static magnetic field. The precessing component induces a signal in the receiving coil if its orientation is appropriate. After an 180° tipping pulse (an “inversion pulse”), the spins on resonance are aligned opposite to the static field and the magnetization relaxes along the static field axis to the equilibrium direction. Hence, a signal will be generated after a 90° tipping pulse, but not after a 180° tipping pulse in a generally uniform magnetic field.
While many different methods for measuring T1 have been developed, a single standard known as the CPMG sequence (Carr-Purcell-Meiboom-Gill) for measuring T2 has evolved. In contrast to laboratory NMR magnets, well logging tools have inhomogeneous magnetic fields due to the constraints on placing the magnets within a tubular tool and the inherent “inside-out” geometry. Maxwell's divergence theorem dictates that there cannot be a region of high homogeneity outside the tool. Therefore in typical well bores, T2*<<T2, and the free induction decay becomes a measurement of the apparatus-induced inhomogeneities. To measure the true T2 in such situations, it is necessary to cancel the effect of the apparatus-induced inhomogeneities. To accomplish the same, a series of pulses is applied to repeatedly refocus the spin system, canceling the T2* effects and forming a series of spin echoes. The decay of echo amplitude is a true measure of the decay due to material properties. Furthermore it can be shown that the decay is in fact composed of a number of different decay components forming a T2 distribution. The echo decay data can be processed to reveal this distribution which is related to rock pore size distribution and other parameters of interest to the well log analyst.
Typically, data bandwidth is limited in a downhole environment. NMR echo trains may include about 1000 data points sampled uniformly over a period, such as 0.6 seconds. Data reduction techniques, including uniform decimation, that are used to meet the bandwidth limitations may result in losing critical information. The present disclosure addresses the problem of achieving reduction of data while preserving all of the critical information in an NMR echo train.